Real-time delay with network coding and feedback

We consider the problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of μμ messages to several receivers. The sender can broadcast a single message or a combination of messages at each timestep, through separate erasure channels. Receivers provide feedback as to whether the transmission was received. If, at some time step, a receiver cannot identify a new message, delay is incurred. Our notion of delay is motivated by real-time applications that request progressively refined input, such as the successive refinement of an image encoded using multiple description coding. Our setup is novel in that it combines coding techniques with feedback information to the end of minimizing delay. We show that it allows Θ(μ)Θ(μ) benefits as compared to previous approaches for offline algorithms, while feedback allows online algorithms to achieve smaller delay compared to online algorithms without feedback. Our main complexity result is that the offline minimization problem is NPNP-hard both under scheduling and coding algorithms. However we show that coding does offer delay and complexity gains over scheduling. We also discuss online heuristics and evaluate their performance through simulations.